Improvement in the texture discrimination task (TDT) depends on sleep, shows feature and retinotopic specificity, varies with stimulus exposure, and is vulnerable to interference. Using a classic interference paradigm, Yotsumoto et al (2009) showed that two-part training on competing background orientations blocked learning of the initial stimulus set. We examined the role of sleep in perceptual interference on a short version of the TDT (to avoid deterioration effects). Interference was tested using two-part training with vertical or horizontal background orientations, which were presented in either the same or different retinotopic locations (lower left and upper right). We examined three nap conditions: naps (with and without rapid eye movement (REM) sleep) compared with quiet rest. We found that quiet rest showed no improvement in the interference condition, whereas naps with REM sleep eliminated interference effects. In fact, REM naps showed more than double the magnitude of learning in the interference condition compared with the non-interference condition. Learning in the interference condition was significantly correlated with the amount of REM sleep in the nap, no other sleep stage was related to performance changes. Interestingly, quiet rest produced perceptual learning to the same degree as sleep in the non-interference conditions. In conclusion, when the brain is serially presented with competing information, such as discriminating a target embedded within two different background orientations, REM sleep appears to enhance memory for information presented first. Thus, the memory trace becomes resilient to interference from subsequent competing targets. Furthermore, although prior studies have compared sleep to active waking controls, we find that quiet rest maybe as effective for learning as REM sleep.